He said there were 19 passengers on board and three crew members. The passengers included two Germans and four Indians, with the remainder Nepali.
Jomsom is a popular trekking destination in the Himalayas about 20 minutes by plane from Pokhara, which lies 200 kilometres (120 miles) west of the capital Kathmandu.
Phanindra Mani Pokharel, a spokesman at the Ministry of Home Affairs, said two helicopters had been deployed for a search operation.
But he said visibility was low.
"The bad weather is likely to hamper the search operation. The visibility is so poor that nothing can be seen," Pokharel said.
Nepal's aviation industry has long been plagued by poor safety due to insufficient training and maintenance.
The European Union has banned all Nepali airlines from its airspace over safety concerns.
The Himalayan country also has some of the world's most remote and tricky runways, flanked by snow-capped peaks with approaches that pose a challenge for even accomplished pilots.
The weather can also change quickly in the mountains, creating treacherous flying conditions.
In March 2018, a US-Bangla Airlines plane crashed near Kathmandu's notoriously difficult-to-approach international airport, killing 51 people.
The flight from the Bangladeshi capital Dhaka crash-landed and skidded into a football field where it burst into flames.
Twenty passengers miraculously escaped the burning wreckage but sustained serious injuries.
An investigation found that the captain suffered an emotional breakdown during the flight, distracting the freshly qualified co-pilot who was at the controls when it crashed.
The report said air traffic control also confused the two ends of the runway, but concluded this had no impact on the flight.
The accident was Nepal's deadliest since 1992 when all 167 people aboard a Pakistan International Airlines plane died when it crashed on approach to Kathmandu airport.
Just two months earlier a Thai Airways aircraft crashed near the same airport, killing 113 people.
In 2019 three people died when a plane veered off the runway and hit two helicopters while taking off near Mount Everest.
The accident happened at Lukla airport which is the main gateway to the Everest region and is reputed to be one of the most difficult in the world for landing and take-off.
Also in 2019 Nepal's tourism minister Rabindra Adhikari was among seven people killed when a helicopter crashed in the country's hilly east.
This month Nepal's second international airport opened at Bhairahawa, aiming to give Buddhist pilgrims from across Asia access to the Buddha's birthplace at nearby Lumbini.
The $76 million project will ease pressure on the overburdened Kathmandu international airport.